%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:26:45 PM UTC 2026
% Result : Theorem 2.41s 1.23s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 75 ( 18 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 83 ( 31 ~; 20 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 69 ( 47 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f6,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f12,conjecture,
? [X0,X1,X2] :
( X2 = X1
& ? [X3] :
( r3(X0,X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplustwoeqy) ).
fof(f13,negated_conjecture,
~ ? [X0,X1,X2] :
( X2 = X1
& ? [X3] :
( r3(X0,X3,X2)
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X1 != X2
| ! [X3] :
( ~ r3(X0,X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r1(X5)
| ~ r2(X5,X4) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK6(X0,X1))
& r3(X0,sK6(X0,X1),sK5(X0,X1))
& sK4(X0,X1) = sK5(X0,X1)
& r2(sK7(X0,X1),sK4(X0,X1))
& r3(X0,X1,sK7(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( r2(X1,sK10(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& sK8(X0,X1) = sK9(X0,X1)
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,X1,sK11(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f6]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 != X2
| ~ r3(X0,X3,X2)
| ~ r2(X4,X3)
| ~ r1(X5)
| ~ r2(X5,X4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f66,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f29]) ).
fof(f74,plain,
! [X2,X3,X0,X4,X5] :
( ~ r1(X5)
| ~ r2(X4,X3)
| ~ r3(X0,X3,X2)
| ~ r2(X5,X4) ),
inference(equality_resolution,[],[f63]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ r2(sK0,X0)
| ~ r3(X2,X1,X3)
| ~ r2(X0,X1) ),
inference(resolution,[],[f64,f74]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ r3(X0,X1,X2)
| ~ r2(sK1(sK0),X1) ),
inference(resolution,[],[f66,f75]) ).
fof(f114,plain,
! [X0] : ~ r2(sK1(sK0),X0),
inference(resolution,[],[f40,f90]) ).
fof(f118,plain,
$false,
inference(resolution,[],[f114,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:59:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.41/1.23 % (1642713)Detected formulas, will run a generic FOF schedule.
% 2.41/1.23 % (1642723)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=897998451:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.41/1.23 % (1642723)First to succeed.
% 2.41/1.23 % (1642723)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1642713"
% 2.41/1.23 % (1642722)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=992071791:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.41/1.23 % (1642722)Also succeeded, but the first one will report.
% 2.41/1.23 % (1642721)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3892553562:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.41/1.23 % (1642719)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=969439882:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.41/1.23 % (1642718)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1624221832:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.41/1.23 % (1642720)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3904821189:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.41/1.23 % (1642721)Also succeeded, but the first one will report.
% 2.41/1.23 % (1642724)dis-21_1_sil=8000:lcm=predicate:random_seed=1282549702:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.41/1.23 % (1642724)Also succeeded, but the first one will report.
% 2.41/1.23 % (1642723)Refutation found. Thanks to Tanya!
% 2.41/1.23 % SZS status Theorem for theBenchmark
% 2.41/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/1.23 % (1642723)------------------------------
% 2.41/1.23 % (1642723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.23 % (1642723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.23 % (1642723)CaDiCaL version: 2.1.3
% 2.41/1.23 % (1642723)Termination reason: Refutation
% 2.41/1.23 % (1642723)Time elapsed: 0.002 s
% 2.41/1.23 % (1642723)Peak memory usage: 89 MB
% 2.41/1.23 % (1642723)Instructions burned: 3 (million)
% 2.41/1.23 % (1642723)------------------------------
% 2.41/1.23 % (1642723)------------------------------
% 2.41/1.23 % (1642713)Success in time 0.271 s
% 2.41/1.23 % Vampire exiting
%------------------------------------------------------------------------------